Orbital phase continuity

Keywords Chemical orbital theory. Electron delocalization. Frontier orbital. Orbital amplitude, Orbital energy, Orbital interaction. Orbital mixing rule, Orbital phase, Orbital phase continuity, Orbital phase environment. Orbital synunetry, Reactivity, Selectivity... 

In 1982 the present author discovered cyclic orbital interactions in acyclic conjugation, and showed that the orbital phase continuity controls acyclic systems as well as the cyclic systems [23]. The orbital phase theory has thus far expanded and is still expanding the scope of its applications. Among some typical examples are included relative stabilities of cross vs linear polyenes and conjugated diradicals in the singlet and triplet states, spin preference of diradicals, regioselectivities, conformational stabilities, acute coordination angle in metal complexes, and so on. 

The electron delocalizations in the linear and cross-conjugated hexatrienes serve as good models to show cyclic orbital interaction in non-cyclic conjugation (Schemes 2 and 3), to derive the orbital phase continuity conditions (Scheme 4), and to understand the relative stabilities (Scheme 5) [15]. 

The orbital phase continuity conditions are summarized in Scheme 4. Cyclic orbital interactions give rise to stabilization when the orbitals simultaneously satisfy the following conditions ... 

The orbital phase continuity conditions stem from the intrinsic property of electrons. Electrons are fermions, and are described by wavefnnctions antisymmetric (change plus and minus signs) with respect to an interchange of the coordinates of an pair of particles. The antisymmetry principle is a more fnndamental principle than Pauli s exclusion principle. Slater determinants are antisymmetric, which is why the overlap integral between t(a c) given above has a negative... 

The orbital phase theory has been developed for the triplet states [19]. The orbital phase continuity conditions (Scheme 4) were shown to be applicable. We describe here, for example, the triplet states of the TMM and BD diradicals, with three a spin electrons and one 3 spin electron. The a and 3 spins are considered separately (Scheme 8). 

Scheme 11 Cyclic orbital interactions and the orbital phase continuity...

The orbital phase theory can be applied to cyclically interacting systems which may be molecules at the equilibrium geometries or transition structures of reactions. The orbital phase continuity underlies the Hueckel rule for the aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions. 

The orbital phase continuity underlies the aromaticity or the thermodynamic stability of cyclic conjugated molecules. Kinetic stability of cyclic conjugate molecules is shown here to be also under the control of the orbital phase property. The continuity conditions can be applied to the design of powerful electron donors and acceptors. 

Scheme 16 The orbital phase continuity controls the regioselectivity...

For the EAG-snbstimted alkenes, the transition states are non-cycUc E-Il-EAG systems. Polarization of Ft, induced by the delocalization from Ft to EAG and E, determines the regioselectivities. The polarization is analogous to that in the TMM dication (Sect. 2.1.4). The cyclic interaction occurs among the electron-accepting orbital eag ) of the substituent, e, n, and n. The a addition is favored by the orbital phase continuity while the P addition is disfavored by the phase discontinuity (Scheme 16). 

The regioselectivities of Diels-Alder reactions are also understood in terms of the orbital phase continuity [29]. The selectivity is also explained by the frontier orbital amplitude [30]. 

Gronert [42] and Schleyer [43] are not aware of our theory [41]. Branched alkanes are stabilized by the C-C bond polarization by two antiperiplanar C-H bonds. The polarization is favored by the orbital phase continuity. We can predict the relative stabilities of alkanes only by counting the number of the vicinal bond trios. Neither the Gronert nor the Schleyer model contains any vicinal interactions. 

Orbital phase continuity for the participation of an electron-donating geminal bond... 

Scheme 43 Orbital phase continuity stabilizes the cw-isomers...

Fig. 5a-c Through-bond interactions in the triplet state of 1,3-diradical, a Mechanism of electron delocalization and polarization of a-spin electrons, b Cyclic orbital interaction, c Orbital phase continuity... 

Orbital phase continuity in triplet state. The orbital phase properties are depicted in Fig. 5c. For the triplet, the radical orbitals, p and q, and bonding n (a) orbital are donating orbitals (labeled by D in Fig. 5c) for a-spin electrons, while the antibonding jt (a ) orbital (marked by A) is electron-accepting. It can be seen from Fig. 5c that the electron-donating (D) radical orbitals, p and q, can be in phase with the accepting (a ) orbital (A), and out of phase with the donating orbital, Jt/a (D) at the same time for the triplet state. So the orbital phase is continuous, and the triplet state of 1,3-diradical (e.g., TMM and TM) is stabilized by the effective cyclic orbital interactions [29, 31]. 

Orbital phase discontinuity in singlet state. In contrast to the triplet state, orbital phase continuity conditions cannot be satisfied simultaneously (denoted by the dashed line in Fig. 6c) in the singlet. Thus, the singlet 1,3-diradical suffers from the orbital phase discontinuity. According to the orbital phase properties, the triplet states of TMM (1) and TM (2) were predicted to be more stable than their singlet states by the orbital phase theory [29, 31]. 

Fig. 8a, b The cyclic orbital interaction (a) and orbital phase continuity (b) in the singlet state of O-type 1,3-diradical... 

To summarize, the properties of triplet and singlet diradicals are closely related to the effectiveness of through-bond and through-space interactions, which are governed by the orbital phase continuity/discontinuity properties. In the next two sections, we will utilize this simple model to predict the spin preference and intramolecular reactivity for a broad range of diradicals. 

On the basis of the orbital phase continuity/discontinuity in the involved cyclic orbital interactions, some general rules were drawn for the Jt-conjugated and localized diradicals ... 

The singlet Kekule diradicals, i.e., the excited state of Kekule molecules, are destabilized by the orbital phase continuity while the triplet Kekule diradicals and the singlet and triplet non-Kekule diradicals are stabilized by the orbital phase continuity. 

Keywords tr-Relaxation o-Relaxation Geminal interaction Inverted bond Lone pair effect Orbital phase continuity Ring strain... 

Decrease of the SE in 71 is the largest of the three cyclopolysilenes. The cyclic (o, o, 71 ) interaction is also favored by the orbital phase continuity [37] and effective... 

Scheme 38 Pentagon stability by cycUc delocalization of a lone pair through vicinal O bonds favored by the orbital phase continuity...

A recent theory of pentagon stability [68, 77] suggests thermodynanic stability of 17 and 18 relative to hexazine. Lone pair electrons in the molecular plane are promoted by the orbital phase continuity to delocalize in a cyclic manner through o bonds of five-membered rings (Scheme 6). The n-rt conjugations also contribute to the relative stability of 17. 

A rather simple extension of the VB method by what is called the orbital-phase continuity principle does permit the qualitative judgment that cyclobutadiene should be less stable than benzene [see W. A. Goddard III, J. Amer. Chem. Soc. 94, 743 (1972), for applications to many processes for which VB theory generally has been regarded as incapable of giving much insight]. 

Inagaki and coworkers46 predicted that the 2-aminoallyl anion resulting from an enamine would be more stable than the corresponding 1-aminoallyl anion on the basis of orbital phase continuity-discontinuity arguments. In support of their hypothesis, deprotonation of the enamine of 1-morpholinocyclohexen-l-ene with -BuLi-TMEDA took place at position 2 rather than at position 3 (equation 25). Their model is also supported by the results of Woodward and coworkers52 for 2-pyrrolidino-1,4-dihydro-naphthalene, which is also deprotonated at the a position. 

As expected, the G-Tj interaction responsible for vicinal delocalization is dependent on conformation. However, relevant calculations reveal that the vicinal delocalization involves the bonding orbital b of the intervening bond B. Inagaki et al. (266, 267) found in addition that the interactions are controlled by orbital phase continuity, namely a- b out of phase, b-rc and fl - c in phase. These requirements were found to be simultaneously satisfied for the ap arrangement, as shown in Figure 36a. In the synperiplanar conformation at least one requirement cannot be met, for example, orbitals a and c are out of phase (Figure 36b). 

Figure 36. Orbital phase continuity control in (a) ap and (b) sp arrangement of three-bond system.

The degree of cyclic electron delocalization has been theoretically proposed to be a function of the mode of donor(D)-acceptor(A) arrangement of the component system as well as orbital phase continuity requirements. A novel notion of continuity-discontinuity of cyclic conjugation shows that there are nondelocalized (4 -f 2)n electron (or nonaromatic) systems and nonlocalized 4n7r electron (or nonantiaromatic) systems in discontinously conjugated systems. The notion was applied to explain the considerable stability of furano- and thieno[3,4-d]thiepines (7) and (8) <77JA7418,78MI 903-01 >. 

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